Calculator.



A. F. ZMHVI.`

CALCULATOR.

APPLICATION FILED APR. 2B. me.

Patent@ 5 SHEEYSY-'SHEU 1A OWN S. 7: ZOTCQIFOQ LO DMMQ@ ZOTrUM A. F, ZAHNI. CALCULATOR.

APPLICATION FLED APR.`2B. 1916..

Patented Dec. 31, 1918.

CALCULATOR.

APPLICATmN FILED APR. 28, 1916.

5 SHEETSWSHEE 4.

wuQ/a/i '50 z- ALEERT F: ZAM@ A. F. ZAHM.

CALCULATOR.

APPLICATON FILED APR. 28. 1916.

Pfemed Dec. 31,1918.

5 SHEETSSHEET 5.

GRM/n0g UNITED STATS FAT 1 ALBERT l". ZAI'IM, OF BUFFALO, NEW YORK.

CALC''LATR.

Specireaten of Letters Patent.

rammen Dee. 31', 1.918.

Application tiled April 2B, 1916. Serial No. 94,136.

To r/Z 'lo/Low. 'it may concern.'

Be it known that l, ALBERT F. Zaini, a

`citizen of the United States, residing at Buf- .,My invention belongs t that class of Y special caluculators designed especially to function in the rapid solution of a particularfabstruse or prolix problem or set of .euch problems related to each other through peculiar sequence of n'iathematical operations. Such instruments are specialties and but a limited number of the large quota utility of my invention has already proven so broad that it finds a high place in Ithis limited group.

The solution of the problems connected with the exact design of aeronautical or other propellers by ordinary means, even allowing for a. most generous use of the slide rule, is at best very arduous and tedious. It is more tedious because the solution is different not only for each dii'crent blade cross section or eainber, but also is further ditferent for each blade station according as that station is distant from the axis of ro iat-ion. Thus, a multiple number of solu tions are necessary not only for blades having different cliarac'teristies and diiferen-t diameters, but also for one and the same Astations along its length.

blade, one for each of a plurality of chosen Moreover, these .solutions involve not simply one factor such as thrust or torque, but a multiple'- number ot' factors, such as helix angle, angle oi' blade incidence (or angle of attack), velocity of translation along the helical path, the ellieieney, etc. The calculator of my invention -not only gives all these values, but gives ing in any way fromits generic spirit.; The

known to the arthave foundwvide use. The.

principal form shown is of a combined ro tatable bar and slide type, but in bothgeneral and detail character it is markedly dif-w ferent from calculators of fore proposed.

0f the drawings: y Figure l is a plan View of one embOi ment, shown largely `in a diagrammetie'fash# ion:

this typehereto Fig. 2 is a longitudinal section ofthe",V

pivoted bar constituting the principal ele'- ment of fthe calculator; y

Fig. 3 is a transverse section of anarm of this bar showing the-mounting or` the slidetherecn g Fig. i is a pian me of astma embode ment Fig. 5 is a transverse-section of the pivoted bar showing the mounting 'of the longitudinal slide thereon;

Fig. 6 is a transverse section of 'an arm of ing the mounting of its longitudinal slide;

Fig. 9 is a transverse section of the longitudinal slide itself showing details of its mounting;

Fig. 10 is a diagram illustrating the forces peitainting to a blade section in operation;

Fig. il is a diagram showing a composition of these forces effected through a transposition adapting lthem for ya solutionby this instrument; v

Fig. l2 is a diagram of a propeller blade; Fig. 13 is a diagram'showing the cross sections of the blade at various distances from its center; l

Fig. il: is e. lift over drift diagram peru taining to a given, blade-section, and i Fig. 15 is a characteristic.tabulation of values obtainable through the useof this in strument. 'y I Referring to Fig. 10, an aerofoil Section A of a form suitable for a propeller blade section is illustrated as being rotated about an yanis OX. We Will-assume 'that this sec.'l

tion is at some distance from the axis, say several feet. velocity of rotation-and BAatlrat of advance,

lf @B represents its-linear then OA represents its true velocity along the helical path, and AOB is the helical angle. The action of the section A on the air produces of itself OC which can be resolved into a lift force OA at right angles to OA and in the general directionof the axis oirotationy OX but not parallel thereto, and a resistance or drift torce AC parallel to OA and 'therefore perpendicular to the lift force 'angle triangles having their hypotenuses and.

one side perpendicular respectively to each other. It is therefore our privilege totake the triangle AOB as a representative to'sc'ale This We do in the -diaf ,gram of Fig. ll andlay. out 'upon the hy y fas arefindeed al? `ofthe' graduations. The

of triangle AOB.

potenuse OA according to sca-le correspondling with that of triangle AOB the lift andH drift forces of the trlahngleUAfC. Obviously, having made this transposition we havebefore us a considerably simplified'diagram,4 yet one from which allthe values of they diagram or" Fig. 10 may be read. It is also clcarthat the forces inaction upon any blade section may be similarlyrepresented. 'Thec'calculator of.' invention. is trranged `in. accordance W'th thetransposition I of Fig; 1l. ln each ofthe embodiments the relation oi'the diagram' of Fig;v .l1 to the instrument is indicatedv by the application of plan View. A' Referring then te the. embodiment of Figs.

l, and 3, and )articularly tor Fig. l, this'g" embodiment comprises a surfaces cross scc-{,-

the reference letters of the' dia'ram to the tioned by the system oi" rectangular cordinates having;n the usual.'decimaljsuils divi'- sions.` Pivotcd to the point fof the-sur-- face S is a har R arranged to swino'- vover the "surface S. This bar is preferably" of. 'colf luloidor other transparcntmaterialand.

bears on its surface u radial line L1 formed by scoring., printingor otheavisej'The -pivot .of thisI bar 4designated generally O is convenience .in manipulation.

i formed bv a' thumb screw oass'ino 'throu l1 an eyelet in bar R and screvvv threaded into an eyclet in surface. Si. The outer lend of vbar R is provided 'with a small k1 ib K for rejecting lupwardly from. the outer end ofthe bar R 'is an. arnrI iii the form ci a sector aboutl the center' O. On this sectoris arranged a the center O. This A form vof a hair, the ed,

slide I connected by taut filament. F with filament may be in the See this arrangement. A right angle slide or T-sqinu'e lQ 1s mounted upon bar .ll inter- "lel to the radial line L. ythe bar R and the arm M is made of trans- *from* the scale Vance. The absciss of the s'ystemare gradthrust if desired and indicated. 'third graduation is made designating the -1 ySpeed of rotationin miles per hour for cach Wire, or any equiv 3 tor the details of' mediate. the center O and the arm M to slide thereover, the side of the bar R enagin the head of the square Q being orme as a straight edge and truly paral- The square Q like parent material and carries thehairline L2 formed in any suitable manner and lying at rightangles to the radial hairline L1 of the bar R.

' The ordinates of the cordinate system of the surface Sare graduated as indicated on the-left margin in units of velocity of advance, the'graduation in this case running from zero to 220 M. P. H. As indicated, these' coordinatesv may also be graduated in j resistance values,` termed resistancev factors.

'However,'thi's scale may be omitteda illustrated, andthe 'resistance factors .deduced `ving the' velocity of advuated, .on .the other hand,` in several differentwayabut acmrdingto correlated scales lowermost series of graduations is in units of blade lengthydenominated Blade stations andy reading from 16V-to 48'by '1ntion represents linear speed of rotation in M.P. H. Along-this same line is liduoif A 'il v bladestation (16, 24, 32 and so on) at of'a plurality of R. P. M. Its gruduationis denominated section R. P. M. By extendingordinate lines from this scale to Vvthevspeed scal'elabove. 'the peripheral speed corresponding to the R. P.`M. is read di'- reotly. v On the iight of the -s stem there .are 'twograduations' by radial ines from the nov vcrements of 8; The uppermost graduu- .center O, the' outer angular-graduation run- .Y

.ning from 5 to 29 and the inner pitch ra'dnation running-.from zero top10 ft. hesel ,graduation's are made according to the tan- Y ents of the'angles representedby thereocity ofg advancedivided bythe. velocity off] rotation at the different stations.4 The iingular graduations therefore -represent lhelifI calangles. f The lineV L 4bears a graduated' scale reir;

resent-ing thelift factor, c". e.-.`-0.(|)0 5 helical/ff(rv sector M bearsradialggraduations to the center O. based upon line` L1 and 'ieuding from zero to .20 in units of-theV tanggnls'of.

'all in a'bsolute units orv other properly. l

chosen correlated units, one hasb'ut to .adj ust- A the three movable elements; bar R, filament Fand scale Q with respect tosurface S and to each other to ascertaln any desired values which a ear in the analytical diagram of Fig; 11. or the base line OB of the surface S represents the base line Ol3r of the dia am of Fi 10- the hairline L of bar Rit e line 0A 0r A of the diagram, and the filament F the line OC of Fig. 11, while the ordinates of surface .S in conjunction withthe line L2 of the square Q complete the pair of'triangles. By simply in the iirst place setting the hairline L according to the speedof rotation of the section of the propeller and the speed. of the machine, both of which are known, in the'second place setting slide Ito place filament F atan angle represented by the drift over lift (D/L) ratio of the' articular blade section being investigate which is-also known, and in the third place setting square/Q at a point where line L2 passes through the point of interi section of the rotative speed chosen vandl the line L1 of br R, 'the following values become immediately readable directly from the instrument;

'1) Section pitch,

" 2 Helical angle,

3 Linear veloeityof rotation, (4 Y True helical velocity, g5 Lift factor, 1 A6 Thrust factor,

'7 Resistance factor,

. 8 'Eihciency "For thetriangles Gab and -Oac are the triangles represented in the vector diagram of Fig. 11 and the scaled dimensions of their sides represent the true solutions of the problem to which the instrument is set. p

The full merit of the invention will best be' comprehended by the workingr out of a detail example by its use. 1

In Fig. 15 Vis a formcommonly used for the tabulation of a large number of values obtained through propeller analysis. `Illustrated inFigs. 12 and 13 is a typical pro peller blade, and the shape ofthe sections f thereof at the various stations which stations arearbitrarily chosen to be 8 apart. The radius of the Asect-ion, that is, its distance from the axis of rotation, is entered in column 1- of the table of Fig. 15. The chord lengths as measured from the sections of Fig. 13 are entered in column 2. The blade angle as measured from the lay-out of these sections, or from the blade itself by suitable measuring instruments, is entered in column 3. i Knowing' the velocity of advance (the forward speed` of the machine). and the- R. P. M, of the driviiflp,f motor (or of the propeller shaft), the helical angles are read on the instrument either at this stage or alater stage. The process consists in simply set; ting the line L1 of bar R to pass through that point defined by the velocity of advance and the velocity of rotation at the particular section or station of the blade beinginvesti-l 'Tand 8 are filled in by values chosen from the lift and drift tables of the known curves with which the blade sections are identified.

' Such known characteristics of certain curves are diagrammatically shown in the drift over lift curves of Fig. 14. Sometimes these values` are not plotted but are given in tables, but it is best to plot them so that intermediate values can be obtained. j

Now, assuming' we are examining the blade section at station 3 of the blade of Fig.4 l2,

thatis, the 24 station, theprocedure is as follows: As shown by the table (Fig. 15) the section at tl1e24:l station has a helicalangle of 17 (this may be determined at this point if not done before) and a drift'over lift coefiicient of .116. Bar R is set with its line L1 at 17 on the outer right hand scale. The slide I is set so that its connected lament F lies at point .116 on the scale of arm M, and the square Q is moved along` bar R until its line L2 crosses the point 60/1400 at which the line L has been set. Preferably the calculations giving the helical angle and the angle of attackare not made until this stage of the operationand in this case the setting' is made directly to the (iO/1400 point defining the velocity of advance yand velocity of rotation, landr the helical angle `17" read and entered at this time, whereupon the angle of attack is obtained and slide I set as explained. This procedure calls for butione handling' of the instrument whereas the other calls for tivo.

The instrument having been set, the reading Oa in the lift factor scale is taken and entered in column 10 of the form ofFig.

15. ts value is 1.037. Thisis a value proportionate to the total lift. It is also proportional to the true blade velocity Which if needed can. be read directly on the same same line L1 as indicated. Next the abscissa of the point c is read on the thrust factor scalo an'd entered in column 11. ,On this suine scale may be read the velocity of yrotation which we iind`is`192 M. P. H. Next the line of the lilamentF is followed until Yit reaches the 100% eiiciency line, which for convenience in designating is located coincident Withthe cordinate whose ordinate is 100 on the speed of advance in M. I. II. scale. This locates a point c2 vertically over c on the line L such vthat the ordinate of e .so .I where Vis-,1n I.'p. s.

is theeiiiciency of the section. This value is approximately 68%'. The eiiiciency of the section is computed by the formula :tan 4:.

am y And 'since the triangles are similar tothetriangles of the original .layout of Figs. 10 and 11, the Values may be read from-the'eliiciency scale. 'an arbitrarily chosen 100% line is quite as exact as .if it were scaled. from the particular triangles in questioninstead of read from similar triangles. .A

''.Ihe values of columns 2, 7, 10 and 11 are multiplied to vobtain column 12; Column 13 is obtained by using the formula thrust eiiiciency where C is a constant.'

, Thereuponl a curve may the values in columns 9, 12, and 13 and the' l areas -inclosed by the thrust curve and4 torque curve ascertained by countingthe` squares, whereupon the following important values may be ascertained by the very. s im-vl .plest calculation.

v'1, 2 and- `3'. The difference lies in the confstruction 'andmountin'g of the slide I and the square Q.' Slide'l isfformed of .glass and lis mountedion arm Mby means of rab' beted side strips t intothe rabbets'oi which project the reduced edges U of the iarm M (Fig. 6).' lThe. square Q1 as' shown kin'Fig.`

5 is similarlysecured to bar R. The'head .k of the square is formed of glass while the body is `preferably.formed of. celluloidor some other less fragile materiall secured thereto.' In the caseof the slideI'the lila.- ment F is secured/to the inner 'side thereof in radial extefy .formcdon the as indicated iiisquarerQ the ine L? on the body of the v squarevis co-incident 'with the'line Scored 'on bar R 'thattlie-bar' Ruis formed in the shape 'cf-a 6 5 sector`. of. a circle about thc ccrerl) thereby This ratio based uponA l setting sidered.

The forli- 1 o-'instrument of Figs. 4.-, 5 and .6 is not generally. the 'same as that of Figs.

'lnndafsquarefarranged on 'said arm' tolie..

moved parallel tothe radius line thereof and-120 v project a line at rigbtangles to saidradiiis, ig.- 6. .In the case'of'tlei A sion '.lof. the radial! lines.

the. .b0dy It atiiight' angles' to. line Llof' Theformbf 7, Sand 9' is a departure" .from that llof t c Apreceding two forms..in4`

eliminating the necessit 'for a branch arm M, slideI and filament .'Y aduations before carried by arm M are ,margin on this sector, and radial lines from' center scored i; A on the surface ,of tlie'transparent bodypl A701 the. bar R take the place of iilamentzgF .j The operation of the instrument is, however substantially the same, there being seiec V that one of the radial lines F2 .which vis designated byl drift over liftratio of '75' the scale, andthis line followed to its interj section with the line Li of the uare Q in the same manner as th'e filament .is so `fol-v lowed ixr the preceding -forms'. The sharpv L point et' t lead pencil will bepfassistance 80 1n this 1section v The are Q' in this embodiment is-p'eculiarly. constructed. The. 'headv lr andthe cated in Fig. 9. f Head thas a rabbeted'e11-v the ti'p'of spring n sliding in a groove and "movingextension g in and out as it passes over the body of the sector.

. Fromthe foregoing itis obvious vthat a large :number of structural modifications 051;' may b'e made bythose s edin the nrt. .Fundamentallyg however,

remainthe same and it is from this fundamental standpoint that the appended` f forth the invention are to be conc- 100.

What I claim is: f l i 1. An instrument of the characterl 'described comprising a planesurface graduated ina system of rectangular cordinates, 105y an arm pivoted at the 'axial center .of said system of cordinates andarranged to' be swept over said surface, asegmental extension of said arnr` graduated angularly 'respect to said axial centerand a'slmre aijilo a el wi ranged l-on said arm to move paci the radius line thereof and proJecting a line*v at right angles tosaid radius.

2,'An instrument of the character d'-,""`l j, lscribed comprising a ,plane' surface gradiigfll-tkgj ated in a system of rectangular.ci'rd1na`t'es` Myy-an armv pivoted at'the'ax'1al'-center, of 'saf1. k

system' so as to be swept over said surface,

A3. An instrument ofi thecharacter de` scribed comprising a lplane surface, a gradl uatedarin to belrotatedfthereover provided y invention will j( of transparent material arranged to be bearing' on its moved along said arm and l to said radius face a line at right angles line.

6. An instrument of the character described comprising a plane surface laid oft` in cordinates, an arm of transparent material Pivoted to acordinate center to be swept over said surface. a graduated radius line drawn across the face of said arm, a square of transparent material arranged to be moved along said arm and 'bearing on its face a line 'at right angles to said radius line, a segmental extension on said arm and a radiall disposed hairline carried by said segmental extension. y

7. An instrument of the character de scribed comprising),` a plane surface, laid out in cordinates graduated according to cor related rotational and translational velocities of .a propeller blade, angular `graduations laid ofi from a given cordinate base line on 'radii 'passing through a coordinate center, an arm pivoted at said cordinate center arranged to sweep' over said surface and having; a radial line graduated to the 40 same scale as said coordinates, said arm hav ing a second graduation for said line in factors according to a scale proportional to but different Jfrom the first said scale, a segmental extension borne by said arm and having anguiar graduations radiated from said axial center and definingr angles based upon the graduated line of said arm, and a square arranged to be moved along said arm and pro ject a line at right angles to the Igraduated line thereof.

8. An instrument of the character described comprisingg a plane surface gradu- 1.ated in rectangular coordinates graduated according to translational and rotational velocities of a propeller, a cordinate line defining between a determinate base line and .itself an arbitrarily chosen 100% cordinate division, an armpivoted at the coordinate center of said base line and arranged to be swept over said surface, a segmental extension borne byV said and radially subdivided into angles, and a square carried by said arm and arranged to project a line at right angles to said arm intersecting said 66 radial subdivision.

9. An instrument of the character described, comprising a surface bearing a system of cordinates, a movable bar connected with said surface arranged to be set to define .angles ou said surfaces, an auxiliary member connected with the first said angle defining member arranged to define angles between said first member and itself. y

1.0. An instrument oi' the character described co-mprising a lsurface bearing a system of' cordinates, a movable bar connected with said surface arranged t0 be set to de fine nuglos on said surface, an auxiliary member connected with the first said angle dening member arranged to define angles between said first member and itself, and a measuring member adjustable along; the

" length ofthe first said angle defining mem ber.

11. An instrument of the character described comprising a surfacegvraduated according to correlated but differently char acterized values and tW'o members movable thereover and coincidently set to define different angles with respect thereto, together with a third movable member carried by one ot the aforesaid movable members and adjustable Ywith respect thereto to deiine units of length of the other two.

12. An instrument ofthe character described comprising a fixed member bearing graduations in correlated values of two quantities, a member movable with respect thereto 'bearing graduation according to the rcsultant of said two quantities and arranged to define angles with respect to the graduations of said fixed member, and :rsecond movable member arranged similarly to the rst, and a third movable member connected with and adjustable with respect to one of the vfirst two. and arranged to define the angular relatidm between the graduations K of said surface and said first two movable members.

13. An instrument of the character described', comprising;r a fixed member having graduations in correlated translational and rotational velocities of a propeller, a member movable over the surface of the first, graduations according to the tangente of angles Whose tangente are represented by the velocity or' translation divided by the velocity of rotation on one of said relatively movable members. and gradual-ions accorciinp: to the drift over lift ratios of propeller sections on thi` other. together with. a third movable member adjustalile linearly' of one of said members, said member to define the linear relation thereof to the other member.

14. An instrument of the character de scribed, a pair of relatively movable members arranged to define angles by their relative movement, a third member movable relatively to the aforesaid pair and arranged to define angles with respect thereto, and a fourth member movable linearly with respect to the others, whereby to define units of length on one at least of the aforesaid members.

15. An instrument, of the character described comprising a pair of relatively movable members arranged to dene combination angles, a third member movable with respect to the pair aforesaid and arranged to define angles in combination With at least one of them, and a fourth member movable with respect to oneofthe aforesaid members and arranged to be set to measure the linear relations of certain' of the aforesaid mem-v bers.

In testimony whereof l aix my signature.

ALBERT it miami 

